Download Holt McDougal Geometry 3-3

3-3 Proving Lines Parallel
Objective
Use the angles formed by a transversal
to prove two lines are parallel.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 1A: Using the Converse of the
Corresponding Angles Postulate
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
4  8
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 1B: Using the Converse of the
Corresponding Angles Postulate
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
Holt McDougal Geometry
3-3 Proving Lines Parallel
The Converse of the Corresponding Angles
Postulate is used to construct parallel lines.
The Parallel Postulate guarantees that for any
line ℓ, you can always construct a parallel line
through a point that is not on ℓ.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 2A: Determining Whether Lines are Parallel
Use the given information and the theorems you
have learned to show that r || s.
4  8
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 2B: Determining Whether Lines are Parallel
Use the given information and the theorems you
have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 3A: Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m
Statements
Holt McDougal Geometry
Reasons
3-3 Proving Lines Parallel
Example 3B
Given: 1  4,
3 and 4 are supplementary.
Prove: ℓ || m
Statements
Holt McDougal Geometry
Reasons
3-3 Proving Lines Parallel
Example 4A: Carpentry Application
A carpenter is creating a woodwork pattern
and wants two long pieces to be parallel.
m1= (8x + 20)° and m2 = (2x + 10)°. If
x = 15, show that pieces A and B are
parallel.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 4B
What if…? Suppose the
corresponding angles on
the opposite side of the
boat measure (4y – 2)°
and (3y + 6)°, where
y = 8. Show that the oars
are parallel.
Holt McDougal Geometry